In the process of wire cut electroerosion, also called traveling-wire electroerosion, a continuous wire electrode is axially transported from supply means, e.g. a reel, to takeup means, e.g. a reel. In the path of wire travel, a workpiece is disposed transversely to the axis of the wire electrode to define a machining gap therewith which gap is flooded with a liquid machining medium, e.g. distilled water. A machining current, typically in the form of a succession of pulses, is passed between the workpiece and the wire electrode across the machining gap to electroerosively remove material from the workpiece. As material removal proceeds, the workpiece carried on a worktable is displaced relative to the wire electrode transversely to the axis thereof which is generally fixed in position along a predetermined path which determines the shape of a contour formed in the workpiece. Over a part of the wire electrode, a pair of guide heads are commonly employed to tightly stretch the traveling wire electrode therebetween and to fix the axis of the wire electrode in a machining position relative to the workpiece. Thus, heretofore any intricate contour as desired has been achieved by displacing the workpiece or the worktable on which it is fixedly mounted relative to the wire electrode which is fixed in its axial position. The workpiece or the worktable must be displaced along the path corresponding to the desired contour and this displacement which directly affects the accuracy of the machined contour requires sophisticated software and hardware to make, convert, process and follow the signals with high precision and consequently makes the process and the apparatus both complicated and expensive.